In order to raise awareness for my interactive social/classifieds site, which is aimed at a local and specific community, I need to advertise with my direct competitors, the local community paper.

The local paper and its web site is run by a community of volunteers and they don't take kindly to anyone, community or not, competing with their own service.

I feel my site is sorely needed because it is free and interactive but if it is used it will generate income through the usual means of paid advertising. However, I don't think my site threatens the advertising revenue for the paper because plenty of people in the community do not use the internet.

So if I am getting opposition from the local paper to advertise my site, how else can I get word out?

Obtain a table or booth at your local Farmer's Market/Craft
Faire/Whatever and demo your app to the userbase directly.

Applying just a small amount of creativity and effort will get around this (very minor) setback in your business plan. Make sure your site has social sharing baked into it so users can help spread the word for you once traffic starts coming in.

And if all of the above fails? Then this statement is demonstrably false:

It is needed because it is interactive but sometimes you don't have enough people in community that need it, as in use the internet. I use the internet and i need it but it's only as useful as how many ppl use it...catch 22.
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frejaJan 23 '13 at 5:23

Right. I know you think it's needed and I don't doubt that something like it probably would be used but the success of getting a population to move from dead tree tech to web tech depends on how motivated that population is to move. If you make a compelling offering and provide a better user experience you will probably be successful with a segment of the audience. How big of a segment? Beats me...you're in a better position to tell. Make a great site, pump it out there as best you can and don't let early setbacks discourage you!
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JCL1178Jan 23 '13 at 5:41